Low inventory method of making eyeglasses

ABSTRACT

A low inventory method of making eyeglasses. Two lens elements having special complementary surfaces are provided. These lens elements can be positioned relative to each other to provide wide ranges of focus correction and astigmatism correction. Various preferred embodiments of the invention are described. In one embodiment the required inventory is only identical sets of two complementary lenses for providing correction for almost all needed eye correction for a typical population. In this embodiment, the lens units are first adjusted relative to each other to provide a desired focusing power. Astigmatism may be corrected by a small adjustment in a second direction perpendicular to the first direction followed by a rotation of the two lenses about the axis of the two lenses. When the adjustments have been made the two lenses are fixed with respect to each other and installed in eyeglass frames. Cutting to the shape of the eyeglass frames can occur either before or after the fixing.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation in part of U.S. patent applicationSer. No. 12/012,743, soon to issue as U.S. Pat. No. 7,943,831 which wasa CIP of Ser. No. 11/607,130, filed Feb. 4, 2008, now U.S. Pat. No.7,325,922, which was a continuation-in-part of Ser. No. 11/085,436 filedMar. 21, 2005, Ser. No. 11/243,944 filed Oct. 5, 2005, Ser. No.11/387,023 filed Mar. 21, 2006 and Ser. No. 11/580,398 filed Oct. 14,2006, each of which are incorporated herein by reference.

FIELD OF INVENTION

This invention relates to eyeglasses, in particular to vision correctingeyeglasses, and to processes for making vision correcting eyeglasses.

BACKGROUND OF THE INVENTION Nearsightedness and Farsightedness

Nearsightedness is a condition of the eye in which distance objectscannot be focused on the retina and farsightedness is a condition of theeye in which near objects cannot be focused on the retina. Theseconditions are normally corrected by eyeglasses lenses having a powerneeded to correct the eye's focus error.

Astigmatism

Astigmatism is a condition of the eye caused by an irregular curvatureof an eye surface, usually the front surface. It can be corrected by aneyeglasses lens in which at least one surface has a different curvaturein different planes through the lens axis.

Thin Lenses

In ophthalmology and optometry it is customary to specify the focallength of spectacle lenses in diopters. The power P of any lens indiopters D is defined as the reciprocal of the focal length f in meters(i.e. P=1/f). For thin lenses, the power P of a two lens (P₁ and P₂)stacked combination is the sum of the power of the two lenses (i.e.,P=P₁+P₂). Stacking of two thin lenses 1 and 2 where P₁=−P₂ would producea power of zero, equivalent to a flat plate. The two lenses do notperfectly cancel, but as long as the power is fairly weak (i.e., lessthan about 5 diopters), the human eye does not detect the residualaberration.

The Human Eye

The adjustable lens of the human eye, called the “crystalline lens”, islocated immediately behind the iris. The crystalline lens is comprisedof 4 layers, from the surface to the center: the capsule, thesub-capsular epithelium, the cortex and the nucleus. The lens capsule isa clear, membrane-like structure that is quite elastic, a quality thatkeeps it under constant tension. As a result, the lens naturally tendstoward a rounder or more globular configuration, a shape it must assumefor the eye to focus at a near distance. Slender but very strongsuspending ligaments, which attach at one end to the lens capsule and atthe other end to protrusions of the circular ciliary body around theinside of the eye, hold the lens in place. When the ciliary bodyrelaxes, the protrusions pull on the suspending ligaments, which in turnpull on the lens capsule around its equator. This causes the entire lensto flatten or to become less convex, enabling the lens to focus lightfrom objects at a far away distance. Likewise when the ciliary musclecontracts, tension is released on the suspending ligaments, and on thelens capsule, causing both lens surfaces to become more convex again andthe eye to be able to refocus on near objects. This adjustment in lensshape, to focus at various distances, is referred to as “accommodation”.The “amplitude of accommodation” of an eye is the maximum amount thatthe eye's crystalline lens can accommodate. This amount is very highwhen young and decreases with age.

The cornea of the human eye is also important in providing focus. Infact, the cornea provides by far the greatest optical power in the eye,with a power of 43.0 D. The entire optical system of the eye has a powerof 58.6 D. This causes the light entering the eye to focus onto theretina. The power of the cornea cannot be adjusted, except by surgery.

Presbyopia

After age 40 in most people (and by age 45 in virtually all people) aclear, comfortable focus at a near distance becomes more difficult witheyes that see clearly at a far distance. This normal condition is knownas “presbyopia”, and is due both to a lessening of flexibility of thecrystalline lens and to a generalized weakening of the ciliary muscle.By the time one reaches 65 or so, the crystalline lens is virtuallyincapable of changing shape. Unless one is nearsighted, it is notpossible to focus objects (such as a printed page) clearly at even anarm's length distance. The amount of presbyopia inevitably increaseswith age. Eyeglasses are usually used to provide correct focus asneeded. These eyeglasses include bifocal, trifocal, and continuous focalglasses. Other solutions include separate glasses for distance andreading.

Alvarez and Mukaijama Adjustable Focus Patents

Luis W. Alvarez patented an adjustable focus lens system in 1967 (U.S.Pat. No. 3,305,294) and another in 1970 (U.S. Pat. No. 3,507,565). Thesepatents are incorporated herein by reference. These patents describelens systems comprised of two complementary lenses. Combining the twolenses produced a lens unit with a focus that could be adjusted byrelative motion of the two lenses in an x direction (i.e. lineardirection) perpendicular to a viewing direction. These adjustable focuslenses have thickness t described by the equation:

t=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y),

or equivalently the by system of relations:

∂³ t/∂x ³=2A,

∂³ t/∂x∂y ²=2A, and

∂³ t/∂x ² ∂y=0.

These equations are hereinafter referred to as the Alverez equations.For this we define the direction away from the face to be the zdirection, the translation direction to be the x direction, and thenon-translation direction to be the y direction. With this, the lenspair has a variable optical power as we translate them differentially inx. This variable power is a function of the distance that we translatethe lenses. The deficiency with the Alvarez equations is that thedescription is too simple for optimal properties. While the equationsare accurate for the region directly in front of the eyes, the glassesare deficient in a number of important optical (especially off-axisimage quality) and other quality (such as thickness and weight) andaesthetic parameters.

A patent issued to Mukaiyama and others in 1997 (U.S. Pat. No.5,644,374) describes essentially the same invention but in a differentway. Applicant has determined that the optical performance for designsaccording to the teachings of this patent to be inadequate. That patenttreats the two lenses as if they behave independently, with power andastigmatism effects essentially summing. Applicant has found thisassumption to be highly inaccurate, except in the case of lenses thatare so weak that they are commercially uninteresting. Also, this patentteaches that the lines of constant power should be parallel and linear,which Applicant has found not to be at all true for an optimized design.

Prior Art Lens Design Techniques Spherical Surfaces—Focus

Lenses generally consist of curved surfaces. The most basic of thesecurved surfaces is a sphere. The curve on the surface of a sphericallens, if extrapolated in all directions, would form a ball or perfectsphere. The sphere would vary in size based on the steepness of thecurve. A steeper, higher power curve would form a smaller sphere with asmaller radius, while a flatter, lower power curve would form a largersphere with a larger radius.

In addition to being described by their power or radius, sphericalcurves also have a direction. An inward curve is called concave, whilean outward curve is called convex. A minus lens that diverges lightwould require a concave spherical surface, while a plus lens thatconverges light would require a convex surface. Therefore, we use theminus (−) sign to denote concave curves, the plus (+) sign to denoteconvex curves, and the term “plano” to describe a flat or zero curve.

A prior art eyeglasses lens has two curved surfaces of consequence tothe vision of the wearer: the front surface and the back surface. Commonlens shapes based on front and back curves are described in the FIG. 21.The corrective power of a lens is determined by adding the front curveto the back curve. This is expressed by the equation: F₁+F₂=F_(Total).For any given corrective power, an infinite number of curve combinationsmay be used to achieve the same result.

Example:

+6.00 D+−2.00 D=+4.00 D

+4.00 D+0.00 D (plano)=+4.00 D

+2.00 D++2.00 D=+4.00 D

Eyeglass fabricators typically have a limited number of curvecombinations with which to work. Lens blanks come from manufacturerswith a limited selection of front curves, also known as base curves,with suggested power ranges for each. Furthermore, since aberrationsoccur as the eye moves away from the optical center of the lens, the labwill choose curves that minimize aberrations. Lenses with curves chosento minimize aberrations are called “corrected curve” or “best form”lenses.

The following chart shows some basic guidelines for selecting basecurves to minimize peripheral aberrations.

Correction Range (Diopters) Power of Front Surface >+12.25 +16.00 D +10.75 to +12.25 +14.00 D   +9.00 to +10.50 +12.00 D  +5.50 to +8.75+10.00 D  +2.25 to +5.25 +8.00 D −1.75 to +2.00 +6.00 D −2.00 to −4.50+4.00 D −4.75 to −8.00 +2.00 D −8.00 to −9.00 +0.50 D  <−9.00 plano orminus

These are guidelines for selecting base curves, there may be many morefactors involved in base curve selection including: manufacturerrecommendations, frame selection, aesthetics, lens material, and patienthistory.

Cylindrical Surfaces—Astigmatism

In addition to the spherical curve, many prescriptions call for acylinder curve to correct for astigmatism. A cylinder curve is curvedalong a single axis and flat along the perpendicular axis. Furthermore,while the focus of a spherical curve is a single point, the focus of acylinder curve is a line. The meridian along which there is no cylinderpower in the lens and consequently the meridian of the cylindrical focusis the cylinder axis. The cylinder axis is expressed in degrees between0 and 180.

Most prescriptions have some combination of spherical and cylindercurves. A lens that combines spherical and cylinder curves is called acompound lens or toric. The convention of the “power cross” helpsconceptualize the compound lens. The power cross is a representation ofthe two major meridians of the lens surface. FIGS. 19 and 20 showexamples where the power in the meridian of the cylinder axis is plano,while the power of the meridian perpendicular to the cylinder axis is+4.00 D.

FIG. 19 shows the +4.00 D cylinder curve at 45°. Note, the curves at the90° and 180° are now +2.00 D and the +4.00 D curve is now at 135°. Asthe meridian is rotated away from the cylinder axis, the curve graduallychanges from 0 to the full power of the cylinder curve (+4.00 D in thisexample) once the meridian is perpendicular to the cylinder axis.

Since a spherical curve is the same in all meridians, if a −2.00 Dspherical curve is combined with a +4.00 D cylinder at 45°, we end upwith a compound lens described by the power cross shown in FIG. 20.

Prior Art Inventory Requirements

The number of lens shapes required to correct a certain population isstatistical in nature, but a reasonable set which would cover a largefraction of people would consist of every power (or focus) value from −6D to +4 D, and every amount and direction of astigmatism from −2 D to +2D. The focus steps could be 0.25 D, and the astigmatism steps 0.5 D.Rather than describing astigmatism as a magnitude and direction, anequivalent description of astigmatism is two components each with signedmagnitudes. These components can be described by zero degreesastigmatism and 45 degrees astigmatism. In this description, for asexample provided in the detailed description, each component would varyfrom −2 D to +2 D in steps of 0.5 D. If the lenses are inventoried asround blanks, then the lens can be rotated before cutting to the shapeof the frame (“edging”). In this case there would need to be (41 powervalues)×(9 astigmatism values)=369 parts. This requires a somewhatexpensive piece of equipment at the point of sale to perform the edging,however. If the lenses are pre-edged in a central factory, then we wouldneed 9 values of 0° astigmatism and 9 values of 45° astigmatism (inaddition to the 41 power values), for a total of 3321 parts. This isusually considered impractical, so most outlets will perform on-siteedging.

What is needed is a way to reduce the number of these parts so that moreof the lens finishing can be done at the central factory and less at thepoint of sale.

SUMMARY OF THE INVENTION

The present invention provides a very low inventory method of makingeyeglasses. Two lens elements having special complementary surfaces areprovided. These lens elements can be positioned relative to each otherto provide wide ranges of focus correction and astigmatism correction.Various preferred embodiments of the invention are described. In oneembodiment the required inventory is only identical sets of twocomplementary lenses for providing correction for almost all needed eyecorrection for a typical population. In this embodiment, the lens unitsare first adjusted relative to each other to provide a desired focusingpower. Astigmatism may be corrected by a small adjustment in a seconddirection perpendicular to the first direction followed by a rotation ofthe two lenses about the axis of the two lenses. When the adjustmentshave been made the two lenses are fixed with respect to each other andinstalled in eyeglass frames. Cutting to the shape of the eyeglassframes can occur either before or after the fixing.

In other embodiments one of the lenses is prefixed in eyeglass framesand the other lens is positioned at the point of sale to provide focusand astigmatism correction. In this embodiment several sets of lensesare needed in inventory, but the needed inventory is a small fraction ofthe inventory requirement of typical prior art laboratories for makingeyeglasses.

In another embodiment one of the lenses is pre-edged but not mounted inthe frame and the other lens is positioned at the point of sale toprovide focus and astigmatism correction. In this embodiment againseveral sets of lenses are needed in inventory, but the needed inventoryis a small fraction of the inventory requirement of typical prior artlaboratories for making eyeglasses.

In a preferred set of embodiments the first of the two lenses iscomprised of rigid material having a special surface. This first lens ispre-edged and mounted in a frame and a second lens comprised of aflexible material adapted to adhere to the first lens by tactileinteractions and having a special surface complementary to the surfaceof the first lens. The second lens is positioned on the first lens toprovide focus and or astigmatism correction.

Preferred General Equations for Thickness Profiles

In preferred embodiments Applicant uses coordinates (u, v) in a planeperpendicular to the viewing direction when looking straight ahead(“on-axis”). He calls this plane the “plane of the lens”. The originpoint (u, v)=(0,0) is defined to be the point directly in front of thepupil when looking straight ahead. This is convenient because users ingeneral desire better performance when the eye is looking on-axiscompared to looking at an angle (“off-axis”). The u-coordinate points inthe direction of relative motion of the lenses when in the nullposition. The v-coordinate direction is orthogonal to the u-coordinatedirection, but in the plane of the lens.

The motion of the lens can either be purely in the u-direction, orrotate around an axis located at (u, v)=(0,−r₀). Applicant uses aparameter α which is 0 in the case of translational motion, and 1/r₀ inthe case of rotation around an axis.

The basic general equations defining the thickness profiles are givenby:

((αv+1)⁻²∂³ t/∂u ³+α(αv+1)⁻¹∂² t/∂v∂u)|_((u,v)=(0,0))=2A

(α³ t/∂v ² ∂u)|_((u,v)=(0,0))=2A

((αv+1)⁻¹∂³ t/∂v∂u ²−α(αv+1)⁻²∂² t/∂u ²)|_((u,v)=(0,0))=0.

The notation “(u, v)=(0,0)” indicates that the relations only hold forthe center point (u, v)=(0,0), but not necessarily outside of thatpoint. However, Applicant requires the thickness profile functions to becontinuous, and the derivatives up to at least third order to becontinuous. Applicant picks A for one lens to be the complement(negative value) of A for the other lens.

The solutions to these equations are:

t=A[uv ²+2(αv+1)(αu−sin(αu))/α³ ]+B[2(αv+1)(1−cos(αu))/α²)]+C[vsin(αu)/α−(αu−sin(αu))/α²)]+Du+E+F(v)+F1(u,v)u ⁴ +F2(v)u ³ v+F3(v)u ² v² +F4(v)uv ³,

whereF(v), F1(u,v), F2(v), F3(v), F4(v)are any functions over the area of the lenses for which derivatives upto at least third order are continuous.

Translation Only Designs:

In the case of translation only designs, α=0. Applicant has defined x=u,and y=v. He defines the origin x=0, y=0 to be the point directly infront of the pupil when looking straight ahead. The equations in thisform for the translation designs are:

(∂³ t/∂x ³)|_((x,y)=(0,0))=2A,

(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A, and

(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0.

Note that the Alvarez description referred to in the Background Sectionis the same at the center (x,y)=(0,0), but Alvarez also applies thisrestriction away from the center point whereas the present inventionconsiders a wide variety of parameters to optimize the design across theentire lens profile. As above Applicant picks A for one lens to be thecomplement of A for the other lens.

The solution is found by taking the limit as α→0 in the above thicknessexpression, which results in

t=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³.

This can be seen as identical to the Alvarez except for the addition ofF1, F2, F3 and F4. These additional functions will be shown in thispatent to be important for optimized performance.

Designs Including Rotation:

The relative motion perpendicular to the viewing direction may alsoinclude rotation in the plane of the lens. In this case, at least one ofthe lenses pivots about a pivot location. For a good solution to exist,this must be outside of the lens perimeter.

For the pivot design, we will call r₀θ=u, and r−r₀=v, with r₀=1/α. Theorigin r=0 is the pivot point, and r=r₀, θ=0 is the point directly infront of the pupil when looking straight ahead. In this form, theequations are given by

r ₀ ⁻¹(r ⁻²∂³ t/∂θ ³ +r ⁻¹ ∂t/∂r∂θ)|_((r,θ)=(ro,0))=2A

r ₀ ⁻¹(∂³ t/∂r ²∂θ)|_((r,θ)=(ro,0))=2A

r ₀ ⁻¹(r ⁻¹∂³ t/∂r∂θ ² −r ⁻²∂² t/∂θ ²)|_((r,θ)=(ro,0))=0.

The solution in this form is

t=Ar ₀[(r ² +r ₀ ²)θ−2rr ₀ sin(θ)]+B2r ₀ r(1−cos(θ))+Cr ₀ [r sin(θ)−r ₀θ]+Dr ₀ θ+E+F(r)+F1(r,θ)r ₀ ⁴θ⁴ +F2(r)r ₀ ³(r−r ₀)θ³ +F3(r)r ₀ ²(r−r₀)²θ² +F4(r)r ₀(r−r ₀)³θ,

The terms have been defined so that the constants are the same as in thegeneral equation, but a shorter equivalent form provided below ispossible by redefining the constants:

t=A′r ² θ+B′r cos(θ)+C′r sin(θ)+D′θ+E′+F′(r)+F1′(r,θ)θ⁴ +F2′(r)(r−r ₀)θ³+F3′(r)(r−r ₀)²θ² +F4′(r)(r−r ₀)³θ.

Choosing Parameters

The choice of parameters to the general solutions depends on desiredoptical performance, other restrictions such as minimum and maximumthickness and aesthetic and other considerations. These specific optimumsolutions use a form much more general than that described by Alvarez.Applicant picks the parameters and functions to optimize lensproperties. In preferred embodiments 17 specific parameters andfunctions are optimized to provide desired performance and other qualityand aesthetic results.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A, 1B and 1C show relative movement of two lens elements in thevertical, horizontal and pivot directions.

FIG. 1D shows the general shape of preferred lens elements and an “eyecenter”.

FIGS. 2A, 2B and 2C and 3A, 3B and 3C show results achieved with thepresent invention.

FIGS. 4A, 4B and 4C show comparison results achieved with a prior arttechnique.

FIGS. 5A and 5B and 5A and 6B show features of another prior arttechnique.

FIGS. 7A and 7B show features of a frame design for horizontal relativelens motion.

FIG. 8 shows a frame design for vertical relative lens motion.

FIGS. 9A through 9I show features of a second frame design for verticallens motion.

FIGS. 10A through 10E show features of a third frame design for verticallens motion.

FIGS. 11A through 11C show features of a fourth frame design forvertical lens motion.

FIGS. 12A through 12D show features of a fifth frame design for verticallens motion.

FIGS. 13A through 13G show features of a frame design for pivital lensmotion.

FIGS. 14A through 14G show features of a second frame design for pivotallens motion.

FIGS. 15A through 15H show features of a third frame design for pivotallens motion.

FIGS. 16A and 16B show a frame system for side to side adjustment.

FIG. 17 show results of a ZEMAX optimization.

FIGS. 18A, B, C and D show features of a preferred embodiment.

FIGS. 19, 20 and 21 show prior art eyeglass design techniques.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS Theory

In preferred embodiments of the present invention focus and astigmatismare corrected by adjusting the position of one of the two lens elements(in each of the two lens units) relative to the other lens element indirections generally perpendicular to a viewing direction. In apreferred set of embodiments the relative motion is linear in a singledirection and in another set of embodiments the relative motion ispivotable about a pivot location outside the lenses. Examples of thisrelative motion are shown in FIG. 1A (vertical motion), FIG. 1B(horizontal motion) and FIG. 1C (pivotal motion). In these examples thefirst lens element has a specially designed thickness profile defining afirst thickness profile and the second lens element has a thicknessprofile defining a second thickness. The thickness profiles are designedsuch that small adjustments of the relative positions of the two lensesin directions perpendicular or approximately perpendicular to a viewingdirection results in changes in the combined focus of the two lenses ofthe lens units.

General Equations for Thickness Profiles

Applicant uses coordinates (u, v) defined in the plane of the lens. Theorigin point (u, v)=(0,0) is defined to be the point directly in frontof the pupil when looking on-axis. This is convenient because users ingeneral desire better performance when the eye is looking nearer tostraight ahead. The u-coordinate points in the direction of relativemotion of the lenses when in the null position. The v-coordinatedirection is orthogonal to the u-coordinate direction, but in the planeof the lens.

The motion of the lens can either be purely in the u-direction, orrotate around an axis located at (u,v)=(0,−r₀). We will use a parameterα which is 0 in the case of translational motion, and 1/r₀ in the caseof rotation around an axis.

The basic general equations defining the thickness profiles are givenby:

((αv+1)⁻²∂³ t/∂u ³+α(αv+1)⁻¹∂² t/∂v∂u)|_((u,v)=(0,0))=2A

(α³ t/∂v ² ∂u)|_((u,v)=(0,0))=2A

((αv+1)⁻¹∂³ t/∂v∂u ²−α(αv+1)⁻²∂² t/∂u ²)|_((u,v)=(0,0))=0.

The notation “(u, v)=(0,0)” indicates that the relations only hold forthe center point (u, v)=(0,0), but not necessarily outside of thatpoint. However, Applicant requires the thickness profile functions to becontinuous, and the derivatives up to at least third order to becontinuous. He picks A for one lens element to be the complement of theother lens element.

The solutions to these equations are:

t=A[uv ²+2(αv+1)(αu−sin(αu))/α³ ]+B[2(αv+1)(1−cos(αu))/α²)]

+C[v sin(αu)/α−(αu−sin(αu))/α²)]+Du+E+F(v)+

F1(u,v)u ⁴ +F2(v)u ³ v+F3(v)u ² v ² +F4(v)uv ³,

whereF(v), F1(u,v), F2(v), F3(v) and F4(v)are any functions over the area of the lenses for which derivatives upto at least third order are continuous.

Translation Only Designs:

In this case α=0. Applicant defines x=u, and y=v. He defines the originx=0, y=0 to be the point directly in front of the pupil when lookingstraight ahead. The equations in this form are:

(∂³ t/∂x ³)|_((x,y)=(0,0))=2A

(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A

(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0.

Note that the Alvarez description is essentially the same at the center(x,y)=(0,0), but is too restrictive away from the center point.Applicant picks A for one lens to be the complement of the other lens.

The solution in found by taking the limit as α→0 in the above thicknessexpression, which results in

t=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³.

This can be seen as identical to the Alvarez except for the addition ofF1, F2, F3 and F4. These additional functions will be shown in thispatent to be important for optimized performance.

Designs Including Rotation:

The motion we consider may also include rotation in the x-y plane. Inthis case at least one of the lenses pivots about a pivot location. Fora good solution to exist, this must be outside of the lens perimeter.

For the pivot design, we will call r₀θ=u, and r−r₀=v, with r₀=1/α. Theorigin r=0 is the pivot point, and r=r₀, θ=0 is the point directly infront of the pupil when looking straight ahead. In this form, theequations are given by

r ₀ ⁻¹(r ⁻²∂³ t/∂θ ³ +r ⁻¹ ∂t/∂r∂θ)|_((r,θ)=(ro,0))=2A

r ₀ ⁻¹(∂³ t/∂r ²∂θ)|_((r,θ)=(ro,0))=2A

r ₀ ⁻¹(r ⁻¹∂³ t/∂r∂θ ² −r ⁻²∂² t/∂θ ²)|_((r,θ)=(ro,0))=0.

The solution in this form is

t=Ar ₀[(r ² +r ₀ ²)θ−2rr ₀ sin(θ)]+B2r ₀ r(1−cos(θ))+Cr ₀ [r sin(θ)−r ₀θ]+Dr ₀ θ+E+F(r)+F1(r,θ)r ₀ ⁴θ⁴ +F2(r)r ₀ ³(r−r ₀)θ³ +F3(r)r ₀ ²(r−r₀)²θ² +F4(r)r ₀(r−r ₀)³θ,

The terms have been defined so that the constants are the same as in thegeneral equation, but a shorter equivalent form is possible byredefining the constants:

t=A′r ² θ+B′r cos(θ)+C′r sin(θ)+D′θ+E′+F′(r)+F1′(r,θ)θ⁴ +F2′(r)(r−r ₀)θ³+F3′(r)(r−r ₀)²θ² +F4′(r)(r−r ₀)³θ.

Choosing Parameters

The choice of parameters to the general solutions depends on desiredoptical performance, other restrictions such as minimum and maximumthickness and aesthetic and other considerations. These specific optimumsolutions use a form much more general than that described by Alvarez.Applicant picks the parameters and functions to optimize lensproperties. In preferred embodiments 17 specific parameters andfunctions are optimized to provide desired performance and other qualityand aesthetic results. These parameters are picked based factors thatmay include:

-   -   The variable optical power is adequate:        -   1. The on-axis optical power at the various settings            (translation distances) should meet the design constraints.        -   2. The off-axis optical power at the various settings may be            allowed to deviate within certain limits. The amount of            deviation will typically be allowed to increase as the            direction becomes more off-axis.    -   The optical performance at all power settings is adequate. This        corresponds to the level of residual aberration at best focus:        -   3. The performance should be particularly good on-axis.        -   4. The off-axis performance may be allowed to degrade within            certain limits. The amount of degradation will typically be            allowed to increase as the direction becomes more off-axis.        -   5. The motion for a given optical power should be minimized.            This is equivalent to maximizing the magnitude of the A            parameter.        -   6. There will be a minimum lens thickness required for            manufacturability and safety.        -   7. The total weight of the lens should be minimized.        -   8. The shape of the front surface most away from the eye            meets certain aesthetic constraints such as a general convex            shape.        -   9. The inner surface closest to the eye is adequately            separated from the eye. The outer surface may also be            constrained to be within a certain distance of the eye for            aesthetic reasons.        -   10. The “average” wedge, which causes a lateral shift in the            image location and possibly chromatic aberration, may be            constrained to be within a certain limit.        -   11. The variable wedge, which causes a lateral shift in the            image location as the power is adjusted, may be constrained            to be within a certain limit        -   12. The wedge, both static and variable, may be matched for            the lens pairs in front of each eye.        -   13. The design should be reasonably insensitive to the exact            eye location relative to the lens within certain limits.            This is to accommodate different face shapes.        -   14. The design may contain a prescription base correction.            This base correction should be preserved as the lenses are            translated into their power settings.        -   15. There may be a surface that is manufactured to a stock            shape, with other surfaces allowed to be designed            differently for various designs. This is in order to reduce            manufacturing costs.

The thickness of the lens element in the above discussion is consideredto be the difference in the front surface and rear surface lensz-location defined as a function of x,y (or u,v or r,θ). Due to bowingor tilting of the lens, there will be a slight difference between thisthickness and thickness alternatively defined as minimum surfaceseparation. It is more conventional in manufacturing to use thez-location definition. While it is important to have the definitionclear for manufacturing, the effect on the constraints is usually veryminor. This is because specifically for eyeglasses, the lenses are closeenough to planar so that minimum thickness is close for the twodefinitions.

In addition to thickness, which is the difference between the surfaces,the lens design also requires the average of the two surfaces to bespecified, which can be called the shape. Applicant places norestrictions on the functional form of the shape, other than the aboveconstraints, and limits to the degree of approximation (forcomputational purposes). In preferred embodiments actually tested withoptical software the constraints were applied with results that arediscussed later.

Balancing Design Constraints

All of these design constraints cannot simultaneously be individuallyoptimized; instead, some balance needs to be chosen by the designer.This can be accomplished algorithmically by combining constraints, forparameters which must be met; and a merit function to be minimized,which contains a functional combination of parameters and creates anoptimal balance based on the weighting of the parameters in the meritfunction.

Adequate Optical Performance

Adequate optical performance is both a design and a manufacturingconsideration. For the case of design, most common is to use thewell-known technique of ray tracing to evaluate performance. Othertechniques include wave optics simulations.

Adequate optical design performance divides into categories:

-   -   1. Optical power at the various settings, on-axis: usually        selected by the designer. This is the amount of focus, usually        expressed in diopters, of the rays entering the eye's pupil.    -   2. Optical power off-axis: this value should match the on-axis        power setting to a degree, but may be allowed to deviate in        order to optimize other lens parameters    -   3. Residual best-focus aberration, no prescription: minimized.        This is the residual ray angular deviation which remains after        focus is removed. The residual aberration will usually be most        constrained on-axis, and allowed to increase as the eye is        pointed increasingly off-axis. This can be expressed in terms of        peak aberration, or in terms of some weighted sum such as rms        aberration.    -   4. The residual best-focus aberration may be designed for a        prescription correction. In this case the residual will be        residual ray angular deviation which remains after focus and        prescription are removed. Usually the prescription correction        includes focus and 2 directions of astigmatism, but may include        higher order terms.

Preferred Technique for Optimization

Applicant presents here a preferred technique for optimizing the lensunits. It should be noted that the numerical techniques involved arestandard, and can be implemented in various ways. Elements of thepresent invention include the application of the desired constraints andmerit functions to the mathematics of lens design, and the more generalvariable thickness profile formulas which allow superior optimization.

Optimization with a Prescription Function:

A design with prescription correction can be optimized using the sameprocedure described above. The only difference is subtraction of the raydirections associated with the desired base prescription before findingthe best focus residual aberration.

Optimization with a Pivot Design:

A pivot design is optimized using the same procedure described above fortranslating lenses. The only difference is 1) the lens thicknessparameters use the formula described above for the pivot design, and 2)the ray trace calculations and spacing calculations are performed on thelenses with the pivot motion rather than translation motion.

Comparison with Prior Art designs:

Applicant prepared a prior art design for comparison purposes. Thisdesign used the more restrictive thickness equations described inAlvarez, but with polynomial terms up to 5^(th) order considered for thecommon shape of the front and back surfaces. This allowed complex shapesbut with the simpler Alvarez thickness formula. Applicant achieved:

-   -   1. average thickness 2.22 mm,    -   2. single-wavelength ray aberration diameter<1.20 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter<0.40 mrad at all        0.25 radian off-axis look angles.

The results are shown in FIGS. 4A, 4B, 4C. Despite being significantlythicker and therefore more massive, the design has worse opticalperformance due to the restrictions on the thickness.

Optimized Design Matching Prior Art Thickness

This design used the general thickness equations described in thispatent. Polynomial terms up to 5^(th) order were considered for thesurfaces. The merit function was adjusted so that the average thicknessmatched the prior art design. We achieved:

-   -   1. average thickness 2.22 mm,    -   2. single-wavelength ray aberration diameter <0.42 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter <0.14 mrad at all        0.25 radian off-axis look angles.

Optimized Design Matching Prior Art Aberration:

This design used the general thickness equations described in thispatent. Polynomial terms up to 5^(th) order were considered for thesurfaces. The merit function was adjusted so that the residualaberrations matched the prior art design. Applicant achieved:

-   -   1. average thickness 1.88 mm,    -   2. single-wavelength ray aberration diameter <1.20 mrad at all        0.5 radian off-axis look angles, and    -   3. single-wavelength ray aberration diameter <0.40 mrad at all        0.25 radian off-axis look angles.

Summary: Alvarez and Mukaiyama Vs Present Invention Alvarez

The performance comparison of a lens unit designed according to thepresent invention versus an Alvarez designed lens unit is summarized inthe following table:

Average Aberration Aberration Thickness (At 0.5 Radians) (At 0.25Radians) Prior Art (Alvarez) 2.22 1.20 0.40 Present Invention 2.00 0.840.28 (Nominal) Present Invention 2.22 0.42 0.14 (Low Aberration) PresentInvention 1.88 1.20 0.40 (Low Weight)

It is clear that the equations described by Alvarez are significantlyinferior to the equations described in this patent.

Mukaiyama

The Mukaiyama patent (1997) treats the two lenses as if they behaveindependently, with power and astigmatism effects essentially summing.Applicant found this assumption to be highly inaccurate. To show this,he first plotted the power diagrams for the back and front lensseparately. See FIGS. 5A and 5B. Notice that the lines of constant powerare not even close to linear, in contrast to a key requirement of theMukaiyama patent.

Also, the Mukaiyama patent makes an implicit assumption that thesevalues simply add together when the lenses are placed in tandem. Here heshows that assumption to be false. See FIGS. 6A and 6B. The first plotis the sum of the above two power diagrams, with contour lines separatedby 0.05 diopters (the numbers were left off for visibility). The secondplot is the actual power diagram for the system. Notice that the twodiagrams do not agree, which shows that it is necessary to consider thelenses as a unit when performing the optimized design.

Zemax Optimization

ZEMAX optical design software was also used to perform the optimizationof the shape of the polynomial surfaces after the thickness profiles hadbeen calculated as described above. The optimization feature in ZEMAXuses an actively damped least squares method and a merit function thatallows for constraints on most optical and physical properties of alens. A root mean square (RMS) spot radius ‘Default Merit Function’ wasused with the additional constraint on the minimum lens thickness of 1.0mm. Due to the non-rotationally symmetric nature of these lenses,multiple operands were required to constrain the lens thickness atseveral radial zones within the lens. The nominal polynomial functionthat provides a desired change in optical focusing power with lateraltranslation tends to have thickness minima in the outer half of thelens, so the constraint on the minimum thickness was defined at zones of60%, 70%, 80%, 90% and 100% of the lens diameter.

A total of 27 configurations were created in a ZEMAX file to model thelens at 9 different eye gaze angles for 3 different lens translationalpositions (0 D, +1 D, +2 D). The merit function was weighted over these27 positions such that the performance was appropriately better at thecentral gaze angles. Specifically, the on-axis gaze angle was weightedat 20, the next 4 closest gaze angles were weighted at 2 and the 4peripheral gaze angles were weighted at 1.

The thickness of the polynomial surface is defined by a 5^(th) orderpolynomial function in x and y. The form of the polynomial function is:

T(x,y)=a ₁ x+a ₂ x ³ +a ₃ xy ² +a ₄ y ⁴ +a ₅ x ² y ² +a ₆ y ⁴ +a ₇ x ⁵+a ₈ x ³ y ² +a ₉ xy ⁴.

In addition to slight eye focus for the off-axis gaze angles, thefollowing polynomial coefficients were free to vary during optimization:a₁, a₂, a₃, a₄, a₅, a₆, a₇, a₈, a₉.

The ratio of a₂ to a₃ was fixed to match the functional form definedabove for the thickness. Only even-powered y terms were used because forthis particular case the lens and view angles were taken to be symmetricin y. This simplified the problem by introducing symmetry. The secondorder terms were omitted, because the lens surface radii of curvaturewere selected as an alternative to use of x² and y² terms.

FIG. 17 is the resulting spot diagrams for the 27 configurations. Theconfigurations correspond to the following lens positions and gazeangles:

Configurations 01-09=+1 D Configurations 10-18=+2 D Configurations19-27=0 D On-Axis (OA) Gaze Angles=Configurations 1, 10, 19 IntermediateGaze (IG) Angles=Configurations 2-5, 11-14, 20-23 Peripheral Gaze (PG)Angles=Configurations 6-9, 15-11, 24-27 Alvarez Concept Adapted forSpherical Coordinates:

In this preferred embodiment, we modify the Alvarez design concepts,which are based on primarily planar lenses with planar motion. This newapproach utilizes spherical lenses with spherical motion. This newspherical design applies to primarily spherical meniscus shaped lenseswith primary motion lateral but along that spherical shell.

The surfaces used are similar to but slightly different from the Alvarezformulas. The Alvarez formulas apply to variable power lenses withlateral motion. This new approach utilizes a variant which allows curvedsurfaces with curved motion, which are more appropriate for eyeglasslenses.

The Alvarez teaching, as a comparison, uses surfaces of the form

A(y ³/3+x ² y)+By+C

for constants A, B, C. The thicknesses of a pair of complementary lensessharing this surface are

A(y ³/3+x ² y)+By+C1 and −A(y ³/3+x ² y)+−By+C2.

When these lenses are translated in the y-direction with respect to eachother, then the sum of the thicknesses becomes

A((y+Δy)³/3+x ²(y+Δy))+B(y+Δy)+C1+−A((y+Δy)³/3+x²(y+Δy))+−B(y+Δy)+C2=2A4Δy(x ² +y ²)+2A(Δy)³/3+2BΔy+C1+C2.

This net thickness describes a powered lens, with power proportional tomotion. When we translate in the x-direction, we likewise produce a netthickness which describes an astigmatic lens.

We use for this new design a similar treatment except that we usespherical coordinates. Our surface, expressed as radial distance r interms of spherical angles θ and φ, has the form

r=AR(sin(φ)cos(θ)−φ cos(θ₀))+R

where R is the base radius of the surface, and A and θ₀ are constants.We use the convention that θ is measured from the equator. The netthickness of a pair of translated lenses as a function of the angles θand φ with relative translation in the φ direction is

AR(sin(φ+Δφ)cos(θ)−(φ+Δφ)cos(θ₀))−R1+−AR(sin(φ−Δφ)cos(θ)−(φ−Δφ)cos(θ₀))+R2=2AR(cos(φ)cos(θ)sin(Δφ)−Δφcos(θ₀))−R1+R2

Where R1 is the radius of the spherical inner lens inner surface and R2is the radius of the spherical outer lens outer surface. If we considerthe thickness as a function of Cartesian coordinates defined on thenominal sphere radius, we see that the thickness can be rewritten as

z≡R sin(θ) and x≡R cos(θ)sin(φ) gives

thickness=2A sin(Δφ)sqrt(R2−z2−x ²)−2ARΔφ cos(θ₀)−R1+R2

Written in this form, the thickness can be seen to describe anellipsoid, which produces power with no astigmatic component.

Also notice the θ₀ parameter in the above surface descriptions affectsthe minimum lens thickness, but not the power, so can be set differentlyfor the two lenses to optimize thickness and weight.

We must also use a standard mathematical routine to convert thespherical description of the surface into a Cartesian array of pointsfor manufacturing. This is done with a search routine that finds θ and φgiven the lateral position in the grid, then finds the r surface valueusing the above formula, and then transforms back to Cartesiancoordinates to compute the depth value.

Index of Refraction Matching:

When the inner and outer lenses are made from different materials, therelationship of the index of refraction of the lenses is important.

-   -   1. In the case where the indices of refraction of the soft and        hard lens are similar enough so that the index mismatch errors        are tolerable, and the above description applies.    -   2. If the soft and hard lenses have index of refraction        different enough to cause index mismatch errors, then the        surface must be made stronger for the lens with a lower index.        In this case the constant A in the surface description        r=AR(sin(φ)cos(θ)−cos(θ₀))+R must be different for each lens,        specifically set proportional to 1/(n−1). The flexibility of the        soft lens will allow the surfaces to still contact.

Tension on the Flexible Lens:

When the soft lens is attached to the hard lens, depending onpositioning, there will be a bending of the soft lens. This bending maybe in a direction which pulls in the center and pushes at the edges,like a suction cup (“Suction Cup Bending”), or may push at the centerand pull at the edges (“Anti-Suction Cup Bending”), or may push at somepoints on the edge and pull on others (“Potato Chip Bending”). The softlens can, however, be designed with a controlled offset radius so thatone of these bending forms will occur for all attachment orientations:

-   -   1. Minimum Bending Design—In this case the surfaces use the same        base radius R so that the lens pair matches in the null        position. The average bending in this case is minimized. Motion        which removes power or adds negative power causes Suction Cup        Bending, a void in the center which is pressed out using the        flexibility of the soft lens. Motion which adds power or removes        negative power causes Anti-Suction Cup Bending, a void at the        edges which must be pushed into contact and affixed. In general        Anti-Suction Cup Bending is more difficult to work with. Motion        which adds astigmatism can cause Potato Chip Bending.    -   2. Suction Cup Only Design—In this case we intentionally use a        larger base radius for the rear design and smaller for the front        design, so that the lens pair forms a Suction Cup Bending type        of arrangement when pressed together for any relative        positioning of the lenses.

To add a base power we change the outer spherical surfaces of one of thetwo lenses. Preferably this would be the hard lens, because the hardlens does not bend and so the attachment issues would not be affected.

Using the Present Invention to Make Fixed-Lens Eyeglasses

The techniques described in this application can be applied to greatlyreduce the cost of providing eyeglasses. These techniques reduce neededinventory stocks of lenses to meet patient's needs for focus andastigmatism correction. These techniques are described below:

In preferred embodiments sets of lenses are prepared as described inparent application Ser. No. 11/607,130, except the lenses are set duringa second stage of a manufacturing process and not adjusted. Theobjective of this is to be able to make many different lensprescriptions with a small number of parts. The parts will be able tocover a range of focus settings. Preferably there will be relativelysmall number of certain, coarsely spaced, focus powers on lens pairsthat are maintained in stock. Fine-tuning will be accomplished bydisplacing the two lenses in the lens pair. The lens pair is then cutand placed into the frames. This process provides for the correction offocus but not astigmatism.

To also provide for the correction of focus and astigmatism a lens pairclosest to the desired focus power is chosen from stock as describedin 1) above. Adjustments are made in a first direction (the x-direction)to provide the desired focus. Then adjustments are made in a y-directionperpendicular to the x-direction to apply astigmatism correction to thelenses. In this case, we need to add a fourth equation to the previousthree equations in the translating x-y form:

(∂³ t/∂x ³)|_((x,y)=(0,0))=2A,

(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A,

(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0,

(∂³ t/∂x ³)|_((x,y)=(0,0))=0.

This last constraint slightly restricts the solution, we now require:

(∂³ F(y)/∂y ³)|_((x,y)=(0,0))=0.

in the thickness formula

t=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³.

As an alternative, matched spherical surfaces can be on the inside.After adjustment, the lenses are glued together (preferably withrefractive index matching glue) as a single unit with no air gap. Thisshould provide a superior mechanical structure, and the internalsurfaces are removed, but the optical performance may be somewhatinferior. If the attached lenses are rigid, then in order to makecontact while still moving the lenses in 2 lateral directions, theinside surfaces must lie on a sphere or plane.

Pre-Fixing One Lens in Frame

In preferred embodiments one of the lenses in each of two two-lens unitsis prefixed in an eyeglass glasses frame prior to delivery to theeyeglasses maker. Since astigmatism typically requires an angularadjustment in this case and since the lenses are moved relative to eachother in two perpendicular directions, both components of astigmatismcannot be achieved with this type of adjustment. As described above weadjust the lenses in x and y, and then rotate the attached set of lensesbefore we cut them out and mount them in the frame. In this case whereone of the lenses is already mounted, we are missing a degree offreedom.

However, astigmatism can be described by two components, oriented 45°from each other. Equivalently, we can describe the same astigmatism by amagnitude and a direction. A given prescription for astigmatism can thusbe created either by creating the proper strength oriented in the properdirection, or adding a given amount of 0° astigmatism to an amount of45° astigmatism. Since focus is azimuthally symmetric, any orientationwill create the same focus.

The direction of astigmatism correction depends on how we oriented thefirst lens in the frame. Therefore, in this embodiment the pre-mountedlenses are provided in various orientations, so that we can get thedirection of astigmatism correct. Another approach is to provide thepre-mounted lenses with different levels of base corrections of thecomponent of astigmatism which we cannot correct with the two directionmovements.

The preferred solution is to have somewhat standard first lensespre-edged for various frames, with a standard astigmatism orientation,and then offer second lenses in various models which provide theastigmatism correction in the direction which we cannot control bylateral shift. This has merit because it requires a minimum amount ofinventory. One approach would be to have a few models of first lenseswith widely spaced focus values for a given frame, and offer flexiblesecond lens inserts which correct for example +−3 diopters of focus and+−3 diopters of 0° astigmatism due to lateral motion. The insert modelscan then be offered at several values of 45° astigmatism, spaced at say0.5 diopter, and (if needed) a few widely spaced values of 0°astigmatism. We will also need a few widely spaced values of focus,which can be part of the first lens or the second lens inserts. If partof the first lens, we may need to cover (−6) to 4 diopter, which couldrequire as few as 2-3 models. Thus the total number of second lensinsert models could be less than 100, maybe as small as 10. The numberof first lens models for each frame could be 1 to a few. There areobviously many ways to mix and match the corrections put into each part.

Flexible Lenses

Flexible lens technology has been developed for stick-on bifocals; seehttp://www.neoptx.com/ or U.S. Pat. No. 6,170,952 that is incorporatedherein by reference. Our concept would be to put the surfaces derivedvia the techniques described herein and in the parent applications ontothe fixed lenses and also onto material similar to that described in the'952. To achieve a prescription correction, the flexible material is cutout with the appropriate lateral shift, and then applied to the fixedlens. The flexible lens can be attached by water or glue.

We have used the materials Texin from Bayer and Pellethane from Dow forthe soft lens. We have used the generic materials Polycarbonate,Acrylic, and Nylon for the hard lenses. In all of these cases thematerial was injection molded into a cavity.

An example is shown in FIGS. 18A, B, C and D. FIG. 19A shows 2 lenseswith the surfaces of the present invention on the inside. If theselenses are rigid, when we translate (with a little rotation); a gapforms as shown in FIG. 18B. If we instead put the special surfaces onthe outside, and have a sphere or cylinder in the middle, the there isno gap as indicated in FIG. 18C. If the bottom lens is flexible,however, then we can bend the back lens so that there is no significantgap even with the special surfaces on the inside as indicated in FIG.18D.

Specific Inventory Examples:

A single hard and soft lens pair is able to correct power with movementin one direction, and one of the two components of astigmatism withmovement in the other direction.

The component of astigmatism depends on orientation. If the lenses arerotated together to accommodate the prescription, the component ofastigmatism can be pointed in the proper direction. If the hard lens ispre-mounted, however, rotation is unavailable, and the missingastigmatism component must be either ignored or corrected by applyingthat component to separate parts.

-   -   1. One Version Fits All: In this case, to cover much of the        population, we would need a large range, typically +4 to −6        diopters. This would require one frame model with hard lenses        mounted and one soft lens model, and would correct power and one        axis of astigmatism.    -   2. Nearsighted/Farsighted Versions: This allows each set to        adjust a smaller region of power, which makes the manufacturing        easier and probably improves quality. There might be a +5 to 0        set and a −1 to −6 set for example. We preferably provide the        base power offset on the hard lens, since it less common for a        patient to have one nearsighted and one farsighted eye. This        would require two frame models with nearsighted or farsighted        hard lenses and one soft lens model. It is possible to put the        base power offset on the soft lens, however.    -   3. Multiple Base Power Versions: There can be more than 2 models        of power if required.    -   4. Multiple Astigmatism Versions for Full Astigmatism        Correction: Our solution for achieving the missing astigmatism        component is to manufacture different models of either the soft        or hard lens with different amounts of this component. We might        typically correct −2 to +2 diopters in ½ diopter steps. This        example would require 9 models of added astigmatism lens. We        prefer to put this component on the soft lens, since we prefer        to supply the hard lenses already mounted in the frames, and the        component will probably be different for each eye. Thus the        number of parts for this case would be 9 soft lens parts and        typically 2 frame parts with mounted hard lens.

An example manufacturing process would be to select frames with rigidfront lens parts which have the base focus nearest to the requirement,then find the flexible back part which has the selected astigmatismcomponent nearest to the requirement, then cut the soft rear lens withthe proper offset to set the power and adjustable astigmatism component,then mount the rear lens onto the front lens.

In order to pick the translation amount between the first and secondlens, any of the following are 4 techniques could be used:

-   -   1. Put fiducials on each lens, such as with stick-ons, and then        move the fiducials a specific distance calibrated to the lens        pair.    -   2. Use a lensmeter to measure the amount of focus and        astigmatism in the lens pair, and adjust to the desired value    -   3. Use templates to cut out the second lens, where the template        is offset the proper amount determined by the calibration of the        lens pair.    -   4. Have the buyer look through the lenses, and adjust the        orientation to most improve the buyer's vision.

Determination of the Lens Offsets to Provide the PrescriptionCorrection:

The following are methods to offset the lenses properly based on thepatient requirements so as to apply the proper amounts of power and/orcylinder correction:

-   -   1. Known Prescriptions, Precut: In this case the required        prescription correction is known. The prescription is converted        based on the lens profile parameters into a horizontal and        vertical attachment offset.    -   2. Known Prescriptions, Postcut: In this case again the        prescription is known. The soft lens is again attached to the        hard lens with the proper offset, but in this case the full soft        lens is attached. After attachment the soft lens is cut such as        with scissors.    -   3. Unknown Prescription, Measure First: In this case the        prescription is unknown, and the offsets are found by the        patient looking through the lenses themselves. The hard lens may        be mounted or unmounted in the frame for the measurement. The        soft lens is moved laterally until the patient has best vision.        The offset is recorded such as by scribing the position. This        recorded offset is then used to position the soft lens.    -   4. Unknown Prescription, Set In Place: In this case the        prescription is again unknown, and the patient again positions        the lenses for best vision correction, but in this case the        lenses are pressed together and attached at least temporarily        while the patient is looking through them. The excess soft lens        around the perimeter is cut away after this attachment.

Adhesion Techniques

-   -   1. Certain materials such as Texin adhere on contact by pressing        to the hard lens. These lenses can be attached through pressing        together with no adhesive. The lens surfaces adhere best when        lightly buffed with a cloth.    -   2. The lenses can be glued through the entire contact region        using standard optical adhesives. Lower cost adhesives such as        dilute wood glue produce an acceptable bond for some        combinations.    -   3. The lenses can be attached around the perimeter with a thin        double-sided tape ring.    -   4. The lenses can be held in place around the perimeters by the        frames, but not attached to each other.    -   5. Use of a Suction Cup Bending design in all of the above cases        can be used.

Commercialization of the Present Invention

Following are some tentative plans for commercializing the presentinvention:

Low Cost Eye Corrections

Fixed lens eyeglasses provided according to the present invention areexpected to be available at relatively low cost as compared to prior artprescription glasses. Therefore Applicants expect a very large marketfor the glasses made up of persons unable or unwilling to purchase theprior art prescription glasses.

Emergency Eyeglasses

Emergency prescription eyewear could be dispensed at places such aspolice stations, military, cruise ships, airlines and drugstores thatconsist of only a few different frame models with pre-mounted frontlenses and a number of flexible back lenses.

Eye Doctor in a Suitcase

The portable eyeglass lab would consist of 1) a suitcase containing 2) ahandheld or portable auto-refractor to determine a patient'sprescription, 3) an assortment of frames with pre-mounted front lenses,4) an assortment of flexible back lens blanks, 5) an assortment of diesmatching the shapes of the offered frames, 6) a die press to cut out theback lens, 7) solution to attach the back lens to the front lens, 8)instruction set or calculation means to indicate which front and backlens to use and how to position the back lens for die cut. Theauto-refractor could be an adjustable frame where the patient selfadjusts the moveable lenses until best vision is achieved. The die anddie press could be replaced with more advanced, programmable deviceslike a vinyl cutter.

Eyeglass Vending Machine

A kiosk containing an assortment of frames with pre-mounted frontlenses, an assortment of back lenses, a vinyl cutter or die cutter, andan assembly machine could be used to dispense readymade prescriptioneyeglasses. The kiosk could contain an eye examination component (eitherobjectively with an auto-refractor, or subjectively via self alignmentof internal lens pairs by the patient), and/or a data input device thatcan accept a patient's prescription values. After inputting prescriptiondata, frame preference, and payment information, robotic devices insidethe kiosk take a frame with correct front lens out of internalinventory, cut the matching back lens according to the prescriptiondata, adhere back lenses to front lenses in the correct position, anddispense custom made eyeglasses.

Prior Art Eyeglass Outlets

In the prior art new eyeglass frames are typically fitted with planolenses for demonstration purposes and to adhere stickers. Many peoplehave such poor vision that they cannot see themselves in the mirror toobserve how they look with the frames they are considering. In oneembodiment of the present invention eyeglass frames are fitted by theframe manufacturer with front lenses of the present invention instead ofplano lenses. The frames are distributed through the usual distributionchannels and end up being displayed in display racks at dispensaries.The dispenser adds the complementary flexible back lens of the presentinvention to provide the patient's sphere equivalent prescription. Thisallows the near or far sighted patient to see him/herself in the mirrorwhile trying out the new frames. Once the patient decides on a frame,either fully correcting lenses or conventional lenses could be fittedinto the frame.

Adjustable Focus Frame Designs

The present invention provides methods for eyeglass makers to offerfixed lens corrective eyeglasses with a minimum of lens inventory. Thisapplication is not directed at adjustable focus frame designs; however,many of the lenses and some of the techniques described above may beapplicable with respect to eyeglasses with adjustable focus framedesigns. Also makers of fixed lens eyeglasses utilizing embodiments ofthe present invention as described above may also desire to offer tosupply their customers with adjustable focus eyeglasses. In this caseframes must be available which can provide relative movement of one orboth of the lenses in each lens unit in order to provide the focusadjustment. Therefore, this section from the parent application Ser. No.11/607,130 is continued in this application.

First Frame Design

A first proposed version of a frame design that permits lateral relativemotion of the lens elements in each lens unit is shown in FIG. 7A. Thisis a drawing of a pair of eyeglasses with wearer operated focusinglenses. A more detailed version of one of the lens units is shown inFIG. 7B. This embodiment includes metal or plastic frame 2, two backlenses 4 and two front lenses 6. Back lenses 4 are mounted rigidly onframe 2. Front lenses 6 are mounted so that they can be moved laterallywith respect to back lenses 4. Two pen mounts 8 are attached rigidly toframe 2 and tabs 10, 12 and 14 are attached rigidly to front lenses 6.Pen 16 passes through pen mounts 8, allowing it to slide through tab 10.Pen 18 passes through frame 2, allowing it to slide through tab 12.Adjustment screw 20 passes through frame 2 and screws into treadedsocket 15 in tab 14. Spring 22 between frame 2 and tab 12 provides acompressive force in the direction of adjustment screw 20. The wearer ofthe glasses shown in FIG. 7A adjusts the focus of each of the lenses byrotating adjustment screws 20 as shown in FIG. 7B.

Techniques for Use

This simple preferred embodiment of the present invention providesimportant improvements over prior art glasses such as bifocals,trifocals and continuous focal lenses. The lens units can each beadjusted by the user so that his viewed object at any distance from afew inches to infinity is exactly in focus. This is especiallyadvantageous if the viewed object is stationary with respect to thewearer such as when reading, working at the computer, watching TV andwatching a movie. Many of the potential embodiments of the presentinventions do not provide for very quick adjustment of the focus. Thiscould be somewhat of a problem in situations, for example, when astudent is watching a lecturer and taking notes at the same time. Asimple solution in these situations, however, would be to provide forseparate adjustment of the two lens units and for the wearer to adjustone lens units to focus on the lecturer and the other lens units tofocus on his notes. His brain will then take over and in each caseproduce images using data from the in-focus eye.

Movement Directions

The lenses can be moved separately or as units. Either lens of a lenspair can be moved, but the preferred approach is to move both lenses inopposite directions to achieve maximum differential movement with aminimum of absolute movement. In addition, the lenses can be adjustedusing actuation from both sides simultaneously, one particular sideonly, or either side. Designs which can be actuated from either sideallow the most ergonomic operation, and such designs with this propertyare described below.

FIG. 1A shows lens movement in the vertical direction. In this case thefront lens element can be moved as a unit, and the back lens elementmoved as a unit. Applicant discusses a variety of approaches toconstrain the motion to the proper displacement.

FIG. 1B shows lens movement in the horizontal direction. In this casethe front lens element can be moved as a unit, and the back lens elementeither fixed or moved as a unit; however, for this case it may bepreferable to connect one front lens to the back lens on the other eye,and vice versa (“crossover”). The crossover movement keeps the motionmore symmetrical between the two eyes.

FIG. 1C shows pivot motion. In this case, as in the horizontal motioncase, the front lens element can be moved as a unit, and the back lenselement either fixed or moved as a unit; however, for this case it maybe preferable to connect one front lens to the back lens on the othereye, and vice versa. The crossover pivot keeps the motion moresymmetrical between the two eyes.

Vertical Movement to Adjust Focus

There are some significant advantages of using vertical adjustment ofthe two lens elements relative to each other to provide focus changes.The principles described above for horizontal adjustment apply equallywell for the vertical adjustment, by interpreting x as the verticaldirection and y as the horizontal direction.

A frame design for vertical relative motion is shown in FIG. 8. In thisdesign, rear frame 100 is positioned on a wearer in the same manner asregular glasses. Front frame 102 is mounted on frame 100 with slideguide 106 and slide slot 108 so that front frame 102 is free to slide upand down relative to rear frame 100 but can not move sideways relativeto rear frame 100. The wearer is able to position front frame 102relative to rear frame 100 by pushing on actuating tab 104 in order toadjust the focus of the lenses. Close tolerances between guide 106 andguide slot 108 hold the front frame in position after it has beenpositioned by the wearer.

FIGS. 9A and 9B show another frame design for adjusting the front frameup and down relatively to the rear frame. In this case slide ring 110that is a part of front frame 116 slides up and down on shaft 112 thatis a part of rear frame 114. The wearer adjusts the relative positionsof the two frames by adjusting pivot bar 118. The earpieces 120 are apart of rear frame 114 and the nose rest 122 is a part of front frame115. Front frame 115 hangs from pivot bar 118 via hang element 121 thatpivots about pivot bar 118 and a pivot connection at nose rest 122 sothat the displacement of frame 116, produced by the pivoting of pivotbar 118, does not alter the spacing between the two frames.

FIGS. 9C through 9I show features of a frame design similar to the onedescribed above. This frame includes back lens assembly 124, front lensassembly 126, a torsion bar assembly 128, two adjusting side bars 130and a nose piece assembly 132 and ear piece 134. The torsion barassembly includes torsion bar 128A two sleeves 128B (through which bar128A is free to pivot) that are rigidly attached to back lens assemblyat locations 128C. Bar 128A is pivotably attached to front lens frameassembly 126 at locations 128D. The two adjusting side bars 130 arepivotably attached to ear piece 134 at location 134A and are attached tofront lens assembly at location 134B as shown in FIG. 9G. Back lensassembly 124 includes peg attachment 124A which is comprised of twocurved pegs as shown in FIG. 9H. Front lens assembly 126 includes twosleeve attachments 126A each attachment having two sleeves that slide ina general up and down direction on the pegs of peg attachment 124A.Preferably the curve of the pegs matches the nominal radius of curvatureof the lenses. This frame also includes nose piece assembly 136 on whichboth front and back lens assemblies rest via sleeves 124B and 126B andstops 136A. With this feature the eyeglasses are positioned based on thelocation of the lowest of the two lens assemblies. Therefore, themovement of the center of the lens units relative to the wearer's eyesmoves only half as far as in the FIG. 8 example. Front lens assembly 126is raised relative to back lens assembly 124 by squeezing bar 130 andearpiece 134 at location 134A and lowered by squeezing at 134B as shownin FIG. 9G. Torsion bar 128 is preferably stiff enough to assure thatthe relative motion of the lens elements in both lens units isapproximately the same. The movement up or down of the front lenselements in one of the lens units relative to the rear lens elementinduces a torque on torsion bar 128A which produces a correspondingmovement in the front lens element in the other lens unit.

FIGS. 10A through 10E show features of a prototype frame design. In thisversion support frame 74 fits on the wearers head just as regularglasses. The lenses, both rear lenses 98R and 98L and front lenses 96Rand 96L are contained in separate frames, rear frame 72 and front frame70, that move relative to support frame 74. Frames 70 and 72 pivot aboutleft and right pivot mounts (left mount 92L and pivot screw 94L areshown). FIG. 11B shows the two lenses aligned. The wearer raises frontlenses 96L and 96R in front frame 70 and lowers rear lenses 98L and 98Rin rear frame 72 to positions such as the one shown in FIG. 11A bysqueezing frame temple arms at position 87 as shown in FIG. 11B. Thewearer moves the lenses in the opposite directions by squeezing frametemple arms at position 85 as shown in FIG. 11B. The result is shown inFIG. 11C.

FIGS. 12A through 12D shows a variation of the FIGS. 10A-E version. TheFIGS. 12A-D version is the same as the FIGS. 10A-E version except thewearer adjusts the relative positions of the lenses by turning cam 60instead of squeezing the temple arms.

Direction of Lens Movement

Preferably the relative motion of the two lens elements in a lens unitis in directions related to the nominal curvature of the lens unit. Forexample if the nominal curvature of the lens unit is 150 mm; theirrelative motion preferably could be along a radius approximately 150 mmbehind the center of the lens unit. However, optical analysis performedby Applicants has shown that tolerances on this issue is loose and (forthe 150 mm nominal curvature example) the lens unit performs acceptablyif the radius is within the range of about 50 mm to infinity (parallelmotion). For embodiments where the nominal curvature of the lenses isflat, relative motion should be parallel. In the examples shown in FIGS.10A through 10E the relative motion of the two lenses is defined byradii of about 50 mm. In the FIG. 8 example a curvature such as 150 mmcould be designed into guide 106 and guide slot 108. In the 9A and 9Bexample the shaft 112 and sleeves 110 could be designed for a curvatureof 150 or any other desired curvature.

Horizontal Movement to Adjust Focus

An example of horizontal motion frames is shown in FIGS. 16A and 16B. Inone of the units, the left rear lens is attached to the right frontlens, an earpiece, and a nosepiece. An identical but mirror-image unitis attached to this unit via a sleeve, allowing horizontal motion.

Pivot Adjustments of Focus

Eyeglasses made with lens pairs that are differentially rotated around apivot point outside of the lenses. The rotation is in a rotation planeapproximately perpendicular to the axes of the lenses and about a pivotpoint in the rotation plane. In embodiments of the present invention thesurface design of the lenses is much more complicated than in theAlvarez type embodiments and the designs described in the parentapplications referred to in the opening sentence of this specification,but the mechanism to move the lenses to achieve desired focusing powerturns out to be simpler and more precise as compared to the linearmovements. The pivot point is preferably equidistant from the two eyes.This preferred rotation point can be the midpoint between the two eyes,or any point above or below the midpoint.

Angular Adjustment with Crossover Pivot Mechanism FIGS. 13A-13G aredrawings showing features of a preferred embodiment providing angularadjustment of the lenses of a set of eyeglasses using a crossover pivotconfiguration. In this configuration the lenses pivot about a pivotmechanism 150 identified in FIGS. 13B and 13G. Nose pieces 152 areattached rigidly to pivot axle 154 in pivot mechanism 150. All fourlenses pivot about pivot mechanism 150. Right front lens 156 is rigidlyattached to left rear lens 158 and left front lens 160 is rigidlyattached to right rear lens 162 so the lenses move in a scissors-likemanner about pivot mechanism 150. The pivot mechanism 150 and theconnections to the lenses and nose piece are shown in FIG. 1G. Each ofthe two ear supports 164 attach to one of the rear lenses in the mannershown in FIG. 13D.Angular Adjustment with Pivoting Front Lenses FIGS. 14A-14G are drawingsshowing features of a preferred embodiment providing angular adjustmentof the lenses of a set of eyeglasses where front lenses pivot relativeto back lenses. In this embodiment both rear lenses are rigidly attachedto the nose piece and hinge-like to ear supports 164. The front lensespivot about pivot 150A. Tab units 166 attached to the front lenses limitrange of movement of the front lenses.Angular Adjustment with Special Pivot Mechanism

FIGS. 15A-15H show detailed design features of a preferred embodimenthaving a special pivot mechanism that can be easily disassemble topermit cleaning of the lens elements. In this design, which is similarthe design shown in FIGS. 13A-13G, the pivot mechanism (as shown in FIG.15H) is provided by two half-sleeves 166 and 168 which are trapped byfront cap 170 and which rotate about a rotation base 172 that is fixedto nose piece 174, with the right front and left rear lens elementsrigidly attached on one half-sleeve and the left front and right rearlens elements rigidly attached on the other half-sleeve. The sleevesbeing trapped by the base and the end cap can only rotate. Some frictionis preferably built in to hold the positions of the lens elements whenno force is being applied. Additional friction can be applied bytightening Philips screw 176 which can also be removed to permitdisassembly and cleaning the inside surfaces of the lens elements.

Advantages of Adjustment about a Pivot Point

The special surface design to provide adjustable focus about a pivotpoint is quite a bit more complicated than the surface design for alinear adjustment. However, as indicated in FIGS. 13A-13G movement ofthe lenses about a pivot point greatly simplifies the frame design toaccomplish the relative lens movements as compared to sliding the lenseslinearly in a linear direction as proposed in Alvarez patents. With thepivot type embodiments, existing frame designs can be used along with asimple pivot type mechanism as shown in FIG. 13G. The pivot design asshown in FIG. 13A-13G assures that all relative movements are perfectlysymmetrical. This is difficult to accomplish with the linear motiontechniques.

Automatic Adjustments of Focus

Several prior art patents have proposed techniques for automaticadjustments of the focus of eyeglass lenses. These techniques attempt todetermine the distance to the viewed object and then automaticallyadjust the focus of the lenses in the eyeglasses based on storedinformation so that the object is in focus for the wearer. Thesetechniques include range finders and small camera viewing both eyes todetect distances between the pupils and small processors and drivers tocalculate distances and control focus based on the calculated distances.Cues from the wearer can also be used as a signal to provide anautomatic adjustment of the focus. For example, a wink of only the righteye could be a cue to increase the length of focus and a wink of onlythe left eye could be a cue to decrease it. Head motion or eyebrowmotion could also be used as a cue. Additional equipment would have tobe added to the basic embodiment described above. Needed would be amotor and actuator with a power source to provide the lateraldisplacement provided in the example by adjustment screw 20. A smallprocessor could be used to translate cues provided by the range finder,camera or wearer into instructions for the motor and actuator. Specificequipment of this general type for determining distances to viewedobjects is described in the patents referenced in the backgroundsection.

As an example, a system can be used to measure inter-pupil distance.This system would provide a determination of the distance of the objectthat the eyes are pointed at. If an object is far away, each eye ispointed in approximately the same direction. As the object moves closer,the eyes start to cross so that both are pointed at the object. Smallcameras can take digital images of each of the eyes and a miniaturedigital processor can compute the offset distance that maximizes thecorrelation of the two images. This offset, when added to the cameraseparation, yields inter-pupil distance. This inter-pupil distance canbe converted by the same digital processor into a range to the object,which is then converted to an offset distance for the sliding lenses.The processor then commands the motor/actuator to position the lenses inthe proper position.

Computer Simulations

Various optical designs based on the present invention have been testedwith computer simulations. Specific simulations were made using computeraided design software available from Zemax Development Corporation withoffices in Bellevue, Wash. Several simulations were made for lens pairswith optical powers of 0 diopter, +2 diopters, and −2 diopters at anglesof 0 degrees, 30 degrees up, 30 degrees down, 30 degrees left and 30degrees right. In all cases the simulations show results that are aboutthe same or better than standard fixed focus prior art spectacle lensesfor correcting focus. Examples of these simulations are discussed abovein the section entitled “ZEMAX Optimization” shown in FIGS. 2A through2C and in FIG. 17.

Variations

Many variations of the specific embodiments described above are possiblewithin the scope of the present invention. For example design codescould be utilized to optimize thicknesses. The Alverez equations couldbe used to provide thickness profiles. Each lens element could include apower base to which the specialized surfaces are applied. One lens ofeach two-lens unit could be fixed in an eyeglass frame prior to deliveryto the eyeglass maker. This could be the front lens or the back lens. Atleast one lens of each two-lens unit may be pre-edged prior to deliveryto the eyeglasses maker. The front and back lenses may be attached toeach other prior to mounting in the eyeglass frame. An uncorrectedcomponent of astigmatism uncorrected by lateral shift may be providedfor by adding that component to various models of one or both lenses.Several models of two-lens units designed to correct astigmatism indifferent directions may be included in the eyeglass maker's inventoryso that the maker can correct astigmatism with a single lateral movementwithout rotation of the lenses. A procedure can be established in whicha customer selects a frame then precut lenses are selected and mountedin the frame and finally the second lenses are attached to the precutlenses to achieve a prescription correction. The second lensalternatively may be attached to the first precut lenses before theprecut lenses are inserted in the frame. The first lenses could bemounted in the frames made available to customers for frame selection.After selection the second lenses are attached. The lenses may be coatedprior to assembly in frames. The contact surfaces between rigid lensescan be a sphere cylinder or plane permitting ease of relative movementbetween the lenses. One of the two lenses in the two-lens units could bemade of a variety of transparent flexible material. A base correctioncan be provided for the two-lens units in the null position. The basecorrection can include a progressive correction, a bifocal correction ora trifocal correction. A variety of lens models can be provided ineyeglass maker's inventory to provide a minimized inventory permitting arange of common corrections by combining part selection and lateralpositioning.

A variety of prior art techniques can be utilized to determine theeyeglass correction needed by customers. These techniques include eyeexamination by an eye doctor resulting in a eyeglasses prescription.Many devices are commercially available for determining correctionneeded. In some cases an adjustable focus frame, of the type disclosedherein and in the parent applications, may be provided to the customerso that the customer can by himself or with the assistance of theeyeglass maker determine the best positioning of the lenses in thetwo-lens units for proper focus and or proper astigmatism correction.The lenses can then be fixed in place after the proper positioning isdetermined. There may be situations where one of the lens units of apair of eyeglasses would be designed for an adjustable focus. The focuscan be near, far or in between. Lateral adjustments can be provided witha micrometer operated by the patient to focus his eyes at variousdistances and having a read-out on a computer screen indicating lenspower needed for focusing at those distances. Such devices might beprovided at drug stores selling inexpensive lenses for reading. Inaddition the lenses might be used to confirm a prescription. In theseadjustable focus frames the lens can move up and down, side to side, orat any other direction predominately perpendicular to the wearer's lineof sight. The moving lenses for each eye can move in common (best for upand down) or in different directions such as out and in away from thenose. Also, both lenses for each eye can move at the same time inopposite directions. Optimized surfaces can be applied to any of thefour surfaces of the two lenses; however, it is best to optimize all ofthe surfaces.

Lens units of the present invention can be utilized in many applicationsother than for eyeglasses. The concepts can be applied to almost anysituation where adjustable focusing is needed. These includemicroscopes, cameras, copy machines and magnifying glasses.

The pivot location does not have to be between the wearer's eyes. Forexample, each lens unit could be designed with a pivot location at theoutside edge of the eyeglasses or at the top or bottom of the lensunits.

Manufacturing techniques that could be employed include: machining (suchas with numerically controlled equipment), molding, casting, curing anduse of gradient index lenses for which thickness is replaced by “opticalpath length” defined by:

(n−1)*(thickness)

where n is the index of refraction. Potential range finders includeoptical, laser and acoustic. Cues for automatic changing of focus couldinclude blinking, eyebrow motion, head motion, and hand switches.

In the preferred embodiments and in the claims, surface shapes aresometimes defined with mathematical equations. Minor modifications tothe equations can be made without causing variations that couldsignificantly adversely affect the performance of the lens systems.Therefore, in his claims Applicant has used the term “approximately” inconnection with these equations with the intention of claiming systemsthat utilize surfaces that are defined by equations that are not exactlythe same as the referenced equations but achieve the same result withinthe tolerance of the lens system as it is being applied. Also, when herefers to A for one lens element being the complement, or “substantiallythe complement”, of A for the other lens element, he means that theirmagnitudes are so close to each other that any difference results ineffects that are within the tolerance of the lens system to which theequations are being applied. When applied to eyeglasses the applicabletolerance is the ability of the human eye to detect a difference.

The reader should understand that the present invention is not limitedto the specific embodiments described above and that many modificationsand additions or deletions could be made to those described embodiments.Therefore, the scope of the invention should be determined by theappended claims and their legal equivalents.

What is claimed is:
 1. A low-inventory method of making eyeglassescomprising the steps of: A) selecting a plurality of two lens units,each lens units comprising a first lens element and a second lenselement wherein the first lens element is rigid and the second lenselement is flexible, wherein the first and second lens elements are eachconfigured to form a respective part of the two lens unit, and whereineach of the first and second lens elements have a thickness profile, andwherein the configurations of the thickness profiles of the first andsecond lenses in each two lens unit enable setting at least one of focusand astigmatism of the two-lens unit by adjustments of the relativepositions of the two lenses in directions approximately perpendicular toa viewing direction; B) adjusting the two lens elements in the selectedtwo-lens unit relative to each other to correct at least one of focusand astigmatism of a patient's eye; C) securing the second flexible lensand the first rigid lens element in fixed relation to one another and aneyeglasses frame.
 2. The low-inventory method as in claim 1 wherein thethickness profiles are approximately given by the following threeequations defining a thickness profile function for each of the two lenselements:((αv+1)⁻²∂³ t/∂u ³+α(αv+1)⁻¹∂² t/∂v∂u)|_((u,v)=(0,0))=2A(α³ t/∂v ² ∂u)|_((u,v)=(0,0))=2A((αv+1)⁻¹∂³ t/∂v∂u ²−α(αv+1)⁻²∂² t/∂u ²)|_((u,v)=(0,0))=0, where A forone lens element to be the complement, or substantially the complement,of the other lens element and where the thickness profile functionscontinuous, and the derivatives up to at least third order arecontinuous.
 3. The low-inventory method as in claim 1 wherein thesolutions to the thickness profile functions are approximately given by:t=A[uv ²+2(αv+1)(αu−sin(αu))/α³ ]+B[2(αv+1)(1−cos(αu))/α²)]+C[vsin(αu)/α−(αu−sin(αu))/α²)]+Du+E+F(v)+F1(u,v)u ⁴ +F2(v)u ³ v+F3(v)u ² v² +F4(v)uv ³, where F(v), F1(u,v), F2(v), F3(v), F4(v) are any functionsover the area of the lenses for which derivatives up to at least thirdorder are continuous and at least one of F1(u,v), F2(v), F3(v) and F4(v)is non zero.
 4. The low-inventory method as in claim 2 wherein saidrelative motion is linear and the thickness profile functions areapproximately given by:(∂³ t/∂x ³)|_((x,y)=(0,0))=2A(∂³ t/∂x∂y ²)|_((x,y)=(0,0))=2A(∂³ t/∂x ² ∂y)|_((x,y)=(0,0))=0, with the solution for each of the twolens elements beingt=A(xy ²+⅓x ³)+Bx ² +Cxy+Dx+E+F(y)+F1(x,y)x ⁴ +F2(y)x ³ y+F3(y)x ² y ²+F4(y)xy ³ where at least one of F1, F2, F3 and F4 is non zero.
 5. Thelow-inventory method as in claim 2 wherein said relative motion ispivotal and the thickness profile functions are approximately given by:r ₀ ⁻¹(r ⁻²∂³ t/∂θ ³ +r ⁻¹ ∂t/∂r∂θ)|_((r,θ)=(ro,0))=2Ar ₀ ⁻¹(∂³ t/∂r ²∂θ)|_((r,θ)=(ro,0))=2Ar ₀ ⁻¹(r ⁻¹∂³ t/∂r∂θ ² −r ⁻²∂² t/∂θ ²)|_((r,θ)=(ro,0))=0, with thesolution for each of the two lens elements being:t=Ar ₀[(r ² +r ₀ ²)θ−2rr ₀ sin(θ)]+B2r ₀ r(1−cos(θ))+Cr ₀ [r sin(θ)−r ₀θ]+Dr ₀ θ+E+F(r)+F1(r,θ)r ₀ ⁴θ⁴ +F2(r)r ₀ ³(r−r ₀)θ³ +F3(r)r ₀ ²(r−r₀)²θ² +F4(r)r ₀(r−r ₀)³θ, where at least one of F1, F2, F3 and F4 arenon zero.
 6. The low-inventory method as in claim 1 wherein the rigidlens in each two-lens unit is fixed in a frame prior to delivery to theeyeglass maker.
 7. The low-inventory method as in claim 1 wherein aplurality of two-lens units are provided in a plurality of modelsadapted to correct astigmatism in different directions in order toachieve the proper astigmatism direction after fixing the two lenses ineyeglasses.
 8. The low-inventory method as in claim 1 and furthercomprising a step wherein an inventory of a plurality of two-lens lensunits are contained in a portable device and used for making eyeglasses.9. The low-inventory method as in claim 1 wherein and further comprisinga step of selling eyeglasses from a vending machine.
 10. Thelow-inventory method as in claim 1 wherein said relative motion of thelenses is primarily along the surface of a sphere.
 11. The low-inventorymethod as in claim 10 wherein surface profiles for the mating surfacesof the first and second lens elements are approximately given by thefollowing equation defining a surface profile function for each of thetwo lens elements:r=AR(sin(φ)cos(θ)−cos(θ₀))+R.
 12. The low-inventory method as in claim 1wherein the indices of refraction of the first and second lens elementsare different, and the relative magnitude of the Alvarez surfaces of thelenses are adjusted to compensate for the index mismatch.
 13. Thelow-inventory method as in claim 1 wherein the flexible lens has amodified base curvature to form a suction cup with the hard lens for allorientations.
 14. The low-inventory method as in claim 6 wherein theflexible lens is cut with the proper offset to achieve a specifiedprescription and then attached to the frame unit by mounting on therigid lens.
 15. The low-inventory method as in claim 6 wherein theflexible lens is attached to the rigid lens with an offset designed toachieve a specified prescription and then cut to remove excess material.16. The low-inventory method as in claim 6 wherein the flexible lensposition is determined by the patient looking through the frame, hardlens, and unattached soft lens, registering the best offset, cutting theflexible lens with said offset, and attaching to the frame unit withmounted rigid lens.
 17. The low-inventory method as in claim 6 whereinthe flexible lens position is determined by the patient looking throughthe frame, rigid lens, and unattached flexible lens, attaching theflexible lens at said offset, and removing an excess portion of theflexible lens material by cutting.
 18. The low-inventory method as inclaim 1 wherein the soft lens material sticks to the hard lens bycontact and is attached by pressing to the hard lens.
 19. Thelow-inventory method as in claim 1 wherein the flexible lens is attachedby gluing to the rigid lens.
 20. The low-inventory method as in claim 1wherein the flexible lens is attached to the rigid lens around theperimeter by pressing to a double-sided tape ring.
 21. The low-inventorymethod as in claim 1 wherein the flexible lens is attached to the frameand not attached to the rigid lens.